I have already studied quantum mechanics (Sakurai and Bransden Atomic/Molecular physics ) and all the relevant quantum field theory (Weinberg I + II, Schwartz and Birrell-Davies).

I'm searching for some references about advanced topics of quantum mechanics, in particular the reference should treat:

  • Entanglement

  • Decoherence

  • Open Quantum Systems

  • Quantum Information

  • Quantum Thermodynamics would be a nice extra

Note: i'm NOT searching for books about Quantum computation and similar, i'm not interested in the computational aspects of it, just on the foundamental concepts.

Both books and lecture notes are welcome, but books are preferred


1 Answer 1


I'm interpreting OP's bulleted list as being interested in quantum foundations and discussion thereof. Therefore, while it's still an "introductory" textbook and doesn't necessarily cover in great detail a lot of the bullet points listed, I think OP should check out Asher Peres' Quantum Theory: Concepts and Methods. Asher Peres could be considered a godfather of quantum information theory, and this book starts with very careful discussions of how to think about quantum mechanics, including operationally, based on some real and thought experiments.

  • Section 1 includes these introductory remarks and the mathematical formulation of quantum mechanics.

  • Section 2 covers composite systems, Bell's Theorem, and contextuality. (So, entanglement goes here, for instance.)

  • Section 3 covers symmetries, information and thermodynamics, semiclassical methods, chaos and irreversibility, and the measuring process.

I suspect this is right up OP's alley, and at the end of every chapter there is a Recommended Reading section, with comments.

The book is wordy (it compares to, say, Ramamurti Shankar's introductory quantum mechanics book, which is heavy on exposition and light on calculation), but it is very clear. Despite this, when there are extended mathematical discussions, they are clear and often push beyond standard quantum mechanics fare. For instance, he discusses the correct mathematical treatment of operators with continuous spectra; he doesn't do this completely rigorously with all of the details (no mention of defect indices here!), because this is not a mathematics textbook, but it's good to see more careful discussions of these issues.

Finally, it is in some places a polemic, and when it is, it is very funny, but this happens rarely, so if you don't want to see disparagement of other treatments of QM, you can gloss over these comments.$^1$. This stems from Peres' epistemic view of quantum states. Asher Peres is probably most well known for his aphorism, "Unperformed experiments have no results," and it's that kind of thinking that underlies this textbook.

$^1$ One example: "Some authors, perceiving conceptual difficulties in the description of the measuring process, have proposed new ways of "interpreting" quantum theory. These proposals are not new interpretations, but radically different theories, without experimental support. This book considers only standard quantum theory$—-$the one that is actually used by physicists to predict or analyze experimental results. Readers who are interested in deviant mutations [emphasis mine] will not be able to find them here."

  • $\begingroup$ Yes, the quantum foundations and all the relative aspects is what i'm more interested in, i'll check the book $\endgroup$
    – LolloBoldo
    Commented Oct 22, 2023 at 18:59
  • $\begingroup$ If no one else posts, I can also suggest another one (in another post): Ballentine. It's more standard than Peres, but it also addresses more foundational issues. It is also polemic, because Ballentine is a cheerleader of the ensemble interpretation of QM, and his book is definitely written with that in mind. $\endgroup$
    – march
    Commented Oct 23, 2023 at 3:23
  • $\begingroup$ Thank you very much! $\endgroup$
    – LolloBoldo
    Commented Oct 23, 2023 at 9:53

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